Which principle is at the core of finite element analysis?

The principle of discretization is fundamental to finite element analysis (FEA) because it allows complex geometries to be broken down into simpler, manageable components called elements. By dividing a complex structure into these finite elements, engineers can analyze the behavior of each element individually using numerical methods. This approximation approach simplifies the mathematical modeling of physical systems, enabling detailed analysis of stress, strain, and deformation within structures.

Discretization helps convert continuous models into discrete forms that can be easily computed. Each element can be treated mathematically, and then the results from all elements are assembled to understand the behavior of the entire structure. This is particularly powerful when dealing with intricate designs and varying material properties since it enables detailed localized analysis where needed.

The other principles, while important in related contexts, do not serve as the core method upon which finite element analysis is fundamentally built. For instance, energy conservation relates to the fundamental physics applied in analyses but is not specific to the process of breaking down geometries. Similarly, strain theory and force equilibrium are concepts used within the solutions derived from finite element models but do not encapsulate the process of analyzing complex geometries through the discretization approach.